SOME REFERENCES Free probability was introduced by Voiculescu in [V1]. However

the reduced free product of C∗–algebras was also considered by Avitzour in [A], (where simplicity was proved under certain hypotheses). An early general reference for many basic topics (free convolution, reduced free product, the free analogue of the Gaussian functor, etc.) and some more advanced topics is the book [VDN]. See also the book by Nica and Speicher [NS] for more combinatorial aspects. For Eric Ricard’s argument that free product of faithful states (or conditional expectations) if faithful, see [I], where it is used with permission. For an example showing that the reduced free product lacks the universal property, see [DR]. For the embedding result, see [BD]. The first appearance of asymptotic freeness in random matrices was in Voiculescu’s pioneering paper [V3]. This was later extended in [D1] and, vastly, in [V7], though none of these contain the nice proof that Speicher presented. Voiculescu’s first appli-cations to free group factors were in [V2]. Rădulescu’s proof that the fundamenta